In response to the European Commission's aim of cutting carbon emissions by 2050, there is a growing need for cutting-edge solutions to promote low-carbon energy consumption in public infrastructures. This paper introduces a Proof of Concept (PoC) that integrates the transparency and immutability of blockchain and the Internet of Things (IoT) to enhance energy efficiency in tangible government-held public assets, focusing on curbing carbon emissions. Our system design utilizes a forecasting and optimization framework, inscribing the scheduled operations of heat pumps on a public sector blockchain. Registering usage metrics on the blockchain facilitates the verification of energy conservation, allows transparency in public energy consumption, and augments public awareness of energy usage patterns. The system fine-tunes the operations of electric heat pumps, prioritizing their use during low-carbon emission periods in power systems occurring during high renewable energy generations. Adaptive temperature configuration and schedules enable energy management in public venues, but blockchains' processing power and latency may represent bottlenecks setting scalability limits. However, the proof-of-concept weakness and other barriers are surpassed by the public sector blockchain advantages, leading to future research and tech innovations to fully exploit the synergies of blockchain and IoT in harnessing sustainable, low-carbon energy in the public domain.